- Resource Library
- Math
- Algebra
- Zero Product Property
- Solving Quadratic Equations With The Zero Product Property And D
Solving Quadratic Equations with the Zero Product Property and D
Presentation
•
Mathematics
•
10th Grade
•
Practice Problem
•
Medium
Charles Dillard
Used 4+ times
FREE Resource
7 Slides • 12 Questions
1
Solving Quadratic Equations with the Zero Product Property and Determining the Number of Solutions
Let’s find solutions to equations that contain products that equal zero.
Let’s use graphs to investigate quadratic equations that have two solutions, one solution, or no solutions.
2
can explain the meaning of the “zero product property.”
I can find solutions to quadratic equations when one side is a product of factors and the other side is zero.
I can explain why dividing by a variable to solve a quadratic equation is not a good strategy.
I know that quadratic equations can have no solutions and can explain why there are none.
3
zero product property
The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0.
4
Dropdown
Here are two ways to define the same function that approximates the height of a projectile in meters, t seconds after launch:
A) h(t) = -5t2 + 27t + 18 B) h(t) = (-5t – 3)(t – 6)
Which way of defining the function allows us to use the zero product property to find out when the height of the object is 0 meters?
5
Fill in the Blanks
Type answer...
6
Multiple Choice
All solutions to (x + 5)(2x – 3) = 0 are.
x = 5 and x = 2/3
x = -5 and x = -3/2
x = -5 and x = -3/2
x=-5 and x = 3/2
7
Solving Quadratic Equations with the Zero Product Property
The zero product property helps us find the solutions to (x – 3)(x + 4) = 0, by showing us that either x-3=0, or x+4 = 0.?
The zero product property only works when the product of the factors is zero. When the product is any other number, we can’t conclude that each factor is that number; therefore why the solutions to (x – 3)(x + 4) = 8 will not be 3 and -4?
Although he expression x2 – x – 12 is equivalent to (x + 3)(x – 4). We cannot apply the zero product property to solve x2 – x – 12 = 0 because the expression is not a product of factors.
You cannot solve the quadratic x2 – x – 12 = 0 by performing the same operation to each side of the equation because doing so doesn’t help us isolate the variable.?
8
Dropdown
9
Dropdown
10
Dropdown
11
Open Ended
If we were solving three equations by graphing.
(x – 5)(x – 3) = 0 (x – 5)(x – 3) = -1 (x – 5)(x – 3) = -4
To solve the first equation, (x – 5)(x – 3) = 0, we need to graph y = (x – 5)(x – 3)
What are the solutions?
12
Open Ended
If we were solving three equations by graphing.
(x – 5)(x – 3) = 0 (x – 5)(x – 3) = -1 (x – 5)(x – 3) = -4
To solve the second equation, we need to rewrite it as (x – 5)(x – 3) + 1 = 0. We then graph y = (x – 5)(x – 3) + 1.
What are the solutions?
13
Open Ended
Solve the third equation (x – 5)(x – 3) = -4 using the previous strategies to find the solutions, what are they?
14
15
Open Ended
Using the previous strategies graph each equation to show the solution. Place a copy of your graph as your answer.
x2 = 121
x2 – 31 = 5
(x – 4)(x – 4) = 0
(x + 3)(x – 1) = 5
(x + 1)2 = -4
16
Dropdown
Do you agree or disagree?
17
(x – 5)(x + 1) = 7
Disagree. Priya solved the equation using the reasoning we would use with the zero product property, but the zero product property only works if the product of two factors is 0. We can tell that 12 isn’t a solution because is 91, not 7.
18
Open Ended
We cannot we use the zero product property to solve x(x – 250) = 100 because the expression on the left does not equal 0.
We can solve x(x – 250) = 100 by graphing
What does the graph tell us about how many solutions and what are they?
(Place a copy of your graph with your answer.)
19
can explain the meaning of the “zero product property.”
I can find solutions to quadratic equations when one side is a product of factors and the other side is zero.
I can explain why dividing by a variable to solve a quadratic equation is not a good strategy.
I know that quadratic equations can have no solutions and can explain why there are none.
Solving Quadratic Equations with the Zero Product Property and Determining the Number of Solutions
Let’s find solutions to equations that contain products that equal zero.
Let’s use graphs to investigate quadratic equations that have two solutions, one solution, or no solutions.
Show answer
Auto Play
Slide 1 / 19
SLIDE
Similar Resources on Wayground
10 questions
Penjumlahan dan Pengurangan Aljabar
Presentation
•
12th Grade - University
14 questions
Solving Rational Equations
Presentation
•
11th Grade
14 questions
Solving Quadratics by Factoring
Presentation
•
9th Grade
14 questions
Exponential Transformations
Presentation
•
9th Grade
15 questions
Systems of Equations Graphs
Presentation
•
9th Grade
14 questions
Angles of Polygons
Presentation
•
9th - 10th Grade
14 questions
Adding, Subtracting & Multiplying Polynomials Review
Presentation
•
9th - 10th Grade
16 questions
Areas of Quadrilaterals
Presentation
•
9th - 10th Grade
Popular Resources on Wayground
24 questions
PBIS-HGMS Day 10
Quiz
•
6th - 8th Grade
10 questions
HCS SCI 03 Summer School Review 3
Quiz
•
3rd Grade
11 questions
Home Scope
Quiz
•
7th - 8th Grade
15 questions
HCS SCI 05 Summer School Assessment 3 Review
Quiz
•
5th Grade
35 questions
Lufkin Road Middle School Student Handbook & Policies Assessment
Quiz
•
7th Grade
18 questions
Geo 11.3 Area of Circles and Sectors
Quiz
•
9th - 11th Grade